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International Mathematics Research Notices (2000) 2000:253-270, doi:10.1155/S1073792800000155
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

The dynamics of zeros of the solitonic Baker-Akhiezer function for the Toda chain

J. F. van Diejen

It is shown that the behavior of the zeros of the stationary solitonic Baker-Akhiezer function for the Toda chain is governed by a discrete-time Ruijsenaars-Schneider system in an external field. The integration of this mapping provides us with an explicit parametrization of the Baker-Akhiezer function. As a by-product, a nonlinear system of Bethe-type equations for the zeros is obtained. The action of the Toda flow gives rise to a motion of the zeros in accordance with the corresponding continuous-time Ruijsenaars-Schneider dynamics.


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